多方通信中的张量秩与强量子非确定性
Tensor Rank and Strong Quantum Nondeterminism in Multiparty Communication
摘要：
本文研究了多方通信中的量子不确定性。在量子计算中有三种（可能）不同类型的非确定性：i）强，ii）经典证明弱，iii）量子证明弱。在这里，我们专注于第一个。强量子非确定性协议以正概率接受正确的输入，并以概率1拒绝不正确的输入。在这项工作中，我们涉及到强量子非确定性多方通信复杂性的通信张量在额头上的数字和手数模型的秩。特别地，通过将de Wolf提出的定义扩展到{ \it非确定性张量秩}，（$nrank$），我们证明了对于任意的布尔函数$f$，当局中人之间不存在先验共享纠缠时：1）在额上数模型中，代价的上界为$nrank(f)$的对数; 2）在手数量模型中，成本的下界是$nrank(f)$的对数。此外，我们表明，当玩家的数量是$o(\log\log n)$，我们有$NQP\nsubseteq BQP$的额头上的数字通信。
英文摘要：
In this paper we study quantum nondeterminism in multiparty communication. There are three (possibly) different types of nondeterminism in quantum computation: i) strong, ii) weak with classical proofs, and iii) weak with quantum proofs. Here we focus on the first one. A strong quantum nondeterministic protocol accepts a correct input with positive probability, and rejects an incorrect input with probability 1. In this work we relate strong quantum nondeterministic multiparty communication complexity to the rank of the communication tensor in the Number-On-Forehead and Number-In-Hand models. In particular, by extending the definition proposed by de Wolf to {\it nondeterministic tensor-rank} ($nrank$), we show that for any boolean function $f$ when there is no prior shared entanglement between the players, 1) in the Number-On-Forehead model, the cost is upper-bounded by the logarithm of $nrank(f)$; 2) in the Number-In-Hand model, the cost is lower-bounded by the logarithm of $nrank(f)$. Furthermore, we show that when the number of players is $o(\log\log n)$ we have that $NQP\nsubseteq BQP$ for Number-On-Forehead communication.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
